Find the Power Set {0,2,4,6}

Problem

𝒫*({0,2,4,6})

Solution

1. Identify the number of elements in the set. The set S={0,2,4,6} has n=4 elements.

2. Determine the total number of subsets. The power set 𝒫*(S) contains 2 elements, so there are 2=16 subsets.

3. List the subsets by size, starting with the empty set ∅

4. Find all subsets with 1 element: {0},{2},{4},{6}

5. Find all subsets with 2 elements: {0,2},{0,4},{0,6},{2,4},{2,6},{4,6}

6. Find all subsets with 3 elements: {0,2,4},{0,2,6},{0,4,6},{2,4,6}

7. Find the subset with 4 elements, which is the set itself: {0,2,4,6}

8. Combine all subsets into a single set to form the power set.

Final Answer

𝒫*({0,2,4,6})={∅,{0},{2},{4},{6},{0,2},{0,4},{0,6},{2,4},{2,6},{4,6},{0,2,4},{0,2,6},{0,4,6},{2,4,6},{0,2,4,6}}

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